The symmetric McMillan map with mixed nonlinearity reduces to two key parameters and yields exact action-angle variables with closed-form rotation number and nonlinear tune shift.
By using its coordinate we can reduce the error above the resonance by approximately 50%
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Dynamics of McMillan mappings III. Symmetric map with mixed nonlinearity
The symmetric McMillan map with mixed nonlinearity reduces to two key parameters and yields exact action-angle variables with closed-form rotation number and nonlinear tune shift.